Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 392 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
4. 4.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 64 cu cm (d) 65 cu cm
5. 5.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 sq cm
6. 6.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
8. 8.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
11. 11.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 36 cu cm (d) 576 cu cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
13. 13.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
16. 16.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
17. 17.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
19. 19.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 576 sq cm (d) 1728 sq cm
20. 20.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 108 sq cm (b) 75 sq cm (c) 300 sq cm (d) 150 sq cm
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
23. 23.A cuboid is 5 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 20 cu cm (b) 16 cu cm (c) 140 cu cm (d) 166 cu cm
24. 24.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
25. 25.A cuboid is 8 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 16 cu cm (b) 92 cu cm (c) 13 cu cm (d) 48 cu cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
27. 27.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 64 sq cm (d) 256 sq cm
28. 28.A cuboid is 8 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 92 cu cm (c) 13 cu cm (d) 48 cu cm
29. 29.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
32. 32.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
33. 33.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 54 cu cm (b) 6 cu cm (c) 14 cu cm (d) 102 cu cm
34. 34.A cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 800 sq cm (b) 400 sq cm (c) 200 sq cm (d) 500 sq cm
35. 35.A cuboid is 10 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 312 cu cm (b) 60 cu cm (c) 360 cu cm (d) 22 cu cm
36. 36.A cuboid is 7 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 142 cu cm (b) 15 cu cm (c) 21 cu cm (d) 105 cu cm
37. 37.A cuboid is 9 cm long, 8 cm wide and 6 cm high. What is its total surface area? (a) 174 sq cm (b) 348 sq cm (c) 432 sq cm (d) 696 sq cm
38. 38.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
40. 40.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times

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